Strategies to increase the arithmetic intensity of the linear solvers

The present work presents a strategy to increase the arithmetic intensity of the solvers. Namely, we profit spatial reflection symmetries to block diagonalise Poisson's equation and split the resulting blocks into a common part plus another subsystem-dependent whose size is, in practice, negligible. By doing so, we reduce the solvers' memory footprint and replace the standard sparse matrix-vector products with the more compute-intensive sparse matrix-matrix product. Then, we present a study about the impact of applying such strategies on different architectures. More concretely, we study how the subsystems' smaller size may make CPUs benefit from larger speedups when solving the decoupled blocks sequentially (due to the resulting greater cache reuse). Conversely, GPUs' lack of cache memory makes them more suitable for implementations based on sparse matrix-matrix products.Adel Alsalti-Baldellou, Xavier ` Alvarez-Farré, Assensi Oliva and F. Xavier Trias have ´ been financially supported by two competitive R+D projects: RETOtwin (PDC2021- 120970-I00), given by MCIN/AEI/10.13039/501100011033 and European Union Next GenerationEU/PRTR, and FusionCAT (001-P-001722), given by Generalitat de Catalunya RIS3CAT-FEDER. Adel Alsalti-Baldellou has also been supported by the predoctoral ` grants DIN2018-010061 and 2019-DI-90, given by MCIN/AEI/10.13039/501100011033 and the Catalan Agency for Management of University and Research Grants (AGAUR), respectively.Postprint (published version